One of my PCs is going to be an agent from another Alpha Complex. I thought it would be fun to give him a secret society that didn't exist in the current Complex with orders to recruit members, and my thought is that he's going to be a Cthulhu cultist. Have any of you done this before? Should I give him a DAIV? Should he have special powers that cost Moxie when he uses them, similar to sanity checks?

(His mutation is that he can sprout twenty venomous tentacles that each get a melee attack. This mutation does not give him any way to get rid of the tentacles once he sprouts them.)

You could give him a DAIV that makes him see/hear Cthulhu instead of Friend Computer when he's contacted by Friend Computer. (Making the Moxie loss more like a sanity loss every time he rolls a Computer on the Computer Die)
Then it could infect the rest of the players making them see the same thing or something different).